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Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and$\unicode[STIX]{x1D707}$–$J$ rheology

Published online by Cambridge University Press:  14 February 2019

Koshiro Suzuki Open the ORCID record for Koshiro Suzuki [Opens in a new window]  and
Hisao Hayakawa
Koshiro Suzuki*
Affiliation:
Simulation & Analysis R&D Center, Canon Inc., 30-2 Shimomaruko 3-chome, Ohta-ku, Tokyo 146-8501, Japan
Hisao Hayakawa
Affiliation:
Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
*
†Email address for correspondence: suzuki.koshiro@mail.canon
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Abstract

A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $\unicode[STIX]{x1D711}$ is developed. The theory successfully derives the critical behaviour in the vicinity of the jamming point (volume fraction $\unicode[STIX]{x1D711}_{J}$), for both the pressure $P$ and the shear stress $\unicode[STIX]{x1D70E}_{xy}$, i.e. $P\sim \unicode[STIX]{x1D70E}_{xy}\sim \dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}^{-2}$, where $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate, $\unicode[STIX]{x1D702}_{0}$ is the shear viscosity of the solvent and $\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}=\unicode[STIX]{x1D711}_{J}-\unicode[STIX]{x1D711}>0$ is the distance from the jamming point. It also successfully describes the behaviour of the stress ratio $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D70E}_{xy}/P$ with respect to the viscous number $J=\dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}/P$.

JFM classification

Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 1125 - 1176
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Copyright
© 2019 Cambridge University Press 

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